Suppose that at the end of each year, revenue for a company was reported as per the table below. What would be the best way to capture the growth over the 5-year period?
| Year | Revenue |
|---|---|
| 2016 | $14,000,000 |
| 2017 | $16,500,000 |
| 2018 | $18,000,000 |
| 2019 | $23,000,000 |
| 2020 | $19,000,000 |
In this context would you simply just add up the growth rate between each year and divide by 4? Or would the CAGR approach be more appropriate? Or would you go with a different method entirely?
Most financial math is more basic than you'd think and it's really focused on comparing periods to each other more than it's about averaging or consolidating information. 5-year averaged or otherwise consolidated "growth" here just hides the big revenue reduction from the prior year.
5 year revenue growth is (19/14)-1 = 36%, but year over year growth is (19/23)-1 = -17%. Really the 5-year number is only interesting if you are comparing it to another rolling 5-year period, the story in your numbers IS the 17% year over year reduction.
And, really, you want these numbers (revenue, assets, liabilities, free cash flow, whatever) on a per-share basis, that way you're controlling for buy-backs and dilution.
You can calculate the annualised time-weighted return ar like so:
r17 = 16.5/14 - 1
r18 = 18/16.5 - 1
r19 = 23/18 - 1
r20 = 19/23 - 1
r = (1 + r17)*(1 + r18)*(1 + r19)*(1 + r20) - 1
ar = (1 + r)^(1/4) - 1 = 7.93 %
This is also the geometric mean return, generally used for consecutive returns.
Also equal to the CAGR (19/14)^(1/4) - 1 = 7.93 %
The arithmetic mean return would tend to overstate the return
(r17 + r18 + r19 + r20)/4 = 9.33 %
See Geometric vs. Arithmetic Mean Return for more detail.
One problem with using the arithmetic mean, even to estimate the average return, is that the arithmetic mean tends to overstate the actual average return by a greater and greater amount the more the inputs vary. ...
Use CAGR
In this context would you simply just add up the growth rate between each year and divide by 4?
No, since linear grow does not scale well. For example, $1M sales growth/year is great when you're a $5M company, but... not so good when you're a $5000M company.
Or would the CAGR approach be more appropriate?
I think so, using the =RRI() function. And I'd compute each individual year's growth so as to compare that with the aggregate growth.
